Jie Ouyang

A mixed corrected symmetric SPH (MC-SSPH) method for computational dynamic problems

Abstract In this work, a mixed corrected symmetric smoothed particle hydrodynamics (MC-SSPH) method is proposed for solving the non-linear dynamic problems, and is extended to simulate the fluid dynamic problems. The proposed method is achieved by improving the conventional SPH, in which the constructed process is based on decomposing the high-order partial differential equation into multi-first-order partial differential equations (PDEs), correcting the particle approximations of the kernel and first-order kernel gradient of SPH under the concept of Taylor series, and finally making the obtained local matrix symmetric. For the purpose of verifying the validity and capacity of the proposed method, the Burgersʼ and modified KdV–Burgersʼ equations are solved using MC-SSPH and compared with other mesh-free methods. Meanwhile, the proposed MC-SSPH is further extended and applied to simulate free surface flows for better illustrating the special merit of particle method. All the numerical results agree well with available data, and demonstrate that the MC-SSPH method possesses the higher accuracy and better stability than the conventional SPH method, and the better flexibility and extended application than the other mesh-free methods.

Simulation of container filling process with two inlets by improved smoothed particle hydrodynamics (SPH) method

In this article, an improved smoothed particle hydrodynamics (SPH) method is proposed to simulate the filling process with two inlets. Improvements are achieved by deriving a corrected kernel gradient of SPH and a density re-initialisation. In addition, a new treatment of solid wall boundaries is presented. Thus, the improved SPH method has higher accuracy and better stability, and conserves both linear and angular momentums. The validity of the new boundary treatment is shown by simulating the spin-down problem. The bench tests are also presented to demonstrate the performance of the improved SPH method. Then the filling process with a single inlet is simulated to show the ability to capture complex-free surface of the proposed method. Finally, the filling process with two inlets is numerically investigated. The numerical results show that the filling patterns are affected significantly by Reynolds number, aspect ratio of the container and the location of the inlets.

An Efficient Dissipative Particle Dynamics-Based Algorithm for Simulating Ferromagnetic Colloidal Suspensions

In this paper, the algorithm, Euler scheme-the modified velocity-verlet algorithm (ES-MVVA) based on dissipative particle dynamics (DPD) method, is applied to simulate a two-dimensional ferromagnetic colloidal suspension. The very desirable aggregate structures of magnetic particles are obtained by using the above-mentioned algorithm, which are in qualitatively good agreement with those in the literature obtained by other simulation methods for different magnetic particle–particle interaction strengths. At the same time, the radial distribution functions of magnetic particles and the mean equilibrium temperatures of the system are also calculated. Next, the mean equilibrium velocities of magnetic and dissipative particles are calculated, by comparing the results obtained by ES-MVVA with those obtained by other algorithm for different time step sizes, it shows the validity and good accuracy of the present algorithm. So, the DPD-based algorithm presented in this paper is a powerful tool for simulation of magnetic colloidal suspensions.

The simpler GMRES method combined with finite volume method for simulating viscoelastic flows on triangular grid

SGMRES(m) integrated with FVM to simulate the viscoelastic fluid flows.Oldroyd-B flow in a planar channel with SGMRES(m) fitting analytical flow.Oldroyd-B flow past a circular cylinder with SGMRES(m) fitting empirical flow.Example applications for small m values being optimal for SGMRES(m) and GMRES(m).Example applications showing that SGMRES(m) could be faster than GMRES(m). An efficient solver integrating the restarted simpler generalized minimal residual method (SGMRES(m)) with finite volume method (FVM) on triangular grid is developed to simulate the viscoelastic fluid flows. In particular, the SGMRES(m) solver is used to solve the large-scale sparse linear systems, which arise from the course of FVM on triangular grid for modeling the Newtonian and the viscoelastic fluid flows. To examine the performance of the solver for the nonlinear flow equations of viscoelastic fluids, we consider two types of numerical tests: the Newtonian flow past a circular cylinder, and the Oldroyd-B fluid flow in a planar channel and past a circular cylinder. It is shown that the numerical results obtained by the SGMRES(m) are consistent with the analytical solutions or empirical values. By comparing CPU time of different solvers, we find our solver is a highly efficient one for solving the flow equations of viscoelastic fluids.

An adaptive method to capture weldlines during the injection mold filling

Weldlines are generally unavoidable during the process of injection mold filling with even moderate complexity when two or more melts meet, which greatly influence the quality of the products. In this paper, we propose a new method to numerically simulate the mold filling process and to capture the weldline adaptively based on the Level Set/Ghost method. The cases where the weldlines are caused by two melt fronts in the injection mold filling process are analyzed, and our special interest is devoted to confirming the position and the shape of the weldline depending on the new adaptive technique based on the level set function. The numerical results show that the proposed method is feasible to detect the influence of the inset size, the inset shape and the inset center place on the weldline.

Multi-scale mathematic modeling of non-isothermal polymeric flow of fiber suspensions

Multi-scale numerical analysis of non-isothermal polymeric flow of fiber suspensions is presented by numerical simulation using a multi-scale modeling. And the multi-scale modeling is established by the coupling of three scales, the macroscopic flow field, the mesoscopic fiber orientation and the microscopic macromolecular information. The constitutive equation which incorporates specific features of polymeric melt of fiber suspensions and its constituents is represented by linear sum of the stress contributions from the three scales. Using the multi-scale modeling, numerical simulations of the polymeric flow of fiber suspensions through a planar contraction cavity and the predicted stress distribution of different scales and fiber orientation are presented. A parametric study based on the fiber aspect ratio, volume fraction and interaction coefficient is used to explore the effects of fiber on system performance. The effects of different inlet temperatures on the stress are also discussed. The present results may elucidate the relationship of the three scales, and exhibit the possibility for developing a meaningful rheological modeling of the polymeric flow of fiber suspensions at the multi-level for industrial application.

Simulation of Stress Distribution near Weld Line in the Viscoelastic Melt Mold Filling Process

Simulations of interface evolution and stress distribution near weld line in the viscoelastic melt mold filling process are achieved according to the viscoelastic-Newtonian two-phase model. The finite volume methods on nonstaggered grids are used to solve the model. The level set method is used to capture the melt interface. The interface evolution of the viscoelastic melt in the mold filling process with an insert in is captured accurately and compared with the result obtained in the experiment. Numerical results show that the stress distribution is anisotropic near the weld line district and the stress distribution varies greatly at different positions of the weld line district due to the complicated flow behavior after the two streams of melt meet. The stress increases quickly near the weld line district and then decreases gradually until reaching the tail of the mold cavity. The maximum value of the stress appears at some point after the insert.

Dynamic Simulation of Fusion Process and Analysis of Flow Field

The level set/ghost method for weldlines in the filling stage of injection molding is introduced in this article. The algorithm is based on non-isothermal, incompressible, generalized Hele-Shaw flow of a viscous fluid. The physical controlling equation systems are numerically simulated by the general finite difference scheme. Tzhe level set/ghost method accurately and efficiently captures the location and shape of the weldlines, whose controlling equations are discretized by the fifth order weighted essentially non-oscillatory (WENO) scheme in space and by the total variation differencing Runge Kutta (TVD-RK) method in time. As a result, the fusion process of weldlines is simulated accurately and the analysis of flow field is given correctly. Examples verify the proposed methodology.The level set/ghost method for weldlines in the filling stage of injection molding is introduced in this article. The algorithm is based on non-isothermal, incompressible, generalized Hele-Shaw flow of a viscous fluid. The physical controlling equation systems are numerically simulated by the general finite difference scheme. Tzhe level set/ghost method accurately and efficiently captures the location and shape of the weldlines, whose controlling equations are discretized by the fifth order weighted essentially non-oscillatory (WENO) scheme in space and by the total variation differencing Runge Kutta (TVD-RK) method in time. As a result, the fusion process of weldlines is simulated accurately and the analysis of flow field is given correctly. Examples verify the proposed methodology.

Numerical study on fiber suspensions in non‐isothermal viscoelastic media

Purpose – The purpose of this paper is to examine the macroscopic and microscopic fields of fiber suspensions in the non‐isothermal situations, also to examine the effect of fiber on this non‐isothermal system.Design/methodology/approach – Control equations are coupled and simultaneously solved by collocated finite volume method on fully triangular meshes.Findings – Temperature dependence and wall temperature have significant effect on both macroscopic and microscopic fields of fiber suspensions. Moreover, the influence of fiber on the non‐isothermal system is similar to that of the isothermal system.Originality/value – This is the first time that the microstructures of both molecules and fibers are presented in the non‐isothermal condition and it is hoped that the results will provide more insight into the microscopics of complex flows.